选取2004—2006年(平稳区间)和2007-2009年(危机区间)全球28支股票指数作为样本,计算标准化后的日对数收益率,利用t分布和正态分布对概率密度分布函数进行拟合.K-S检验显示,t分布的拟合优度高于正态分布.计算股指对数收益率t分布的自由度数v和标度参数b.研究表明:股票指数的风险在金融危机期间大幅升高;在平稳期,自由度v一般大于2,中位数为2.64,与“自由度近似等于3”的结论相符,但是金融危机期间,股票指数大幅波动,自由度v一般小于2,t分布曲线的性质发生改变.由于中国对股票交易设立了涨跌停板制度,上证综指和深圳成指的v值在金融危机前后没有显著变化,均在3附近.
This research selected 28 main stock indexes of the world as a sample, in which the year of 2004-2006 was viewed as stable period, and the year of 2007-2009 was viewed as crisis period. The probability density distributions of daily logarithmic returns were fitted with normal distribution curves and t-distribution curves, calculated with the number of freedom degrees v and scale parameter b. The Kolmogorov-Smirnov test shows that t-distribution fits the data better than normal distribution. The investigation shows that the risks of stock markets are much higher during the financial crisis. During the stable period, almost all the v-values are larger than 2 with the medium of 2.64, in accordance with that v-value is approximately 3 in existing literatures. During the financial crisis, v-values are smaller than 2 in most cases, except China, and the characters of t distribution curves have been changed. Because of the variation limit polity in Shenzhen and Shanghai Stock markets, there are no significant variations of v-values for Chinese stock indexes, which are approximately 3 before and after financial crisis.